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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: not (empty_p x0).
Apply unknownprop_d74508268cf2245bb4de852843c85bf4733bd48f6383eaac9c68dfae0d149115 with 707e2.. (4326e.. x0), x0.
Let x1 of type ι be given.
Apply iffI with prim1 x1 (707e2.. (4326e.. x0)), prim1 x1 x0 leaving 2 subgoals.
Assume H1: prim1 x1 (707e2.. (4326e.. x0)).
Claim L2: 4326e.. x0 x1
Apply unknownprop_381047c913ae030e9e9942d1a8901abc4d96b713731a5b7b04cd06cd75bdfe7a with 4326e.. x0, x1 leaving 2 subgoals.
The subproof is completed by applying unknownprop_87135efbd349f82ea798668ead3e3c95927d5ac9bf1fcb9052c1dff107e96de8 with x0.
The subproof is completed by applying H1.
Apply unknownprop_81e2497d53f26977fa8ca722fab407ecbd3aa74818556ba29653e265699cc106 with x0, x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying L2.
Assume H1: prim1 x1 x0.
Apply unknownprop_ef71c7659631e6712550b179497e8718243f15729bbc2ba1fccf8bb659c5df87 with 4326e.. x0, x1 leaving 2 subgoals.
The subproof is completed by applying unknownprop_87135efbd349f82ea798668ead3e3c95927d5ac9bf1fcb9052c1dff107e96de8 with x0.
Apply unknownprop_547d526f8f61234c156e3c73fa4a8a1aa9a628b58fe16fb380304ebbca858804 with x0, x1.
The subproof is completed by applying H1.